10n^2-100=-15

Solution for 10n^2-100=-15 equation:

10n^2-100=-15

We move all terms to the left:

10n^2-100-(-15)=0

We add all the numbers together, and all the variables

10n^2-85=0

a = 10; b = 0; c = -85;
Δ = b2-4ac
Δ = 02-4·10·(-85)
Δ = 3400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3400}=\sqrt{100*34}=\sqrt{100}*\sqrt{34}=10\sqrt{34}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{34}}{2*10}=\frac{0-10\sqrt{34}}{20}
=-\frac{10\sqrt{34}}{20}
=-\frac{\sqrt{34}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{34}}{2*10}=\frac{0+10\sqrt{34}}{20}
=\frac{10\sqrt{34}}{20}
=\frac{\sqrt{34}}{2}
$